00:02
Welcome to calculus methods.
00:04
Now previously we've looked
extensively in differentiationfrom first principles.
00:09
And we've also now observed
a much faster way ofdifferentiating.
00:14
In this lecture, we are now
going to take faster methodand we are actually going to
start looking at someapplication of differentiation.
00:21
So, we're going to go over
the differentiation basics today.
00:28
We'll look at the standard
method of differentiation whichis the faster method that
we've just spoken about.
00:34
And we'll practice it
with few more questions.
00:37
And then we're going to move
on to more exciting bitswhich are the applications
of it.
00:41
So we're going to look at
gradients of a particular pointon a curve.
00:45
How to find equations
of tangents.
00:47
How to find equations
of normals.
00:49
And again this is really useful
for courses like medicinewhere you are actually looking
at gradients of curves.
00:56
So that you can work out
and the steepnessor the speed, that things are growing or decaying with.
01:03
So previously we have found
the gradient of a functionlike this 3x(squared) + 5x-1
using the definitionof first principles.
01:12
We applied the really long
formula and cameto the final answer.
01:16
Where we made the delta X or
the limit of delta X go to 0.
01:21
But thankfully to modern
calculus we now have muchfaster ways of doing this.
01:25
And we discuss that faster way
previously where you bringthe power down and multiply it,
and you decrease the power by 1.
01:32
Remember what we said that any
constants at the end go to 0or they just disappear.
01:40
As a little recap we will have
a look at the general ruleonce again.
01:44
So if you have a function
y = x to the power of n.
01:49
You bring the power down
as the multipleof X to the power of n
as we do here.
01:55
And then you decrease
the power by 1.
01:58
So the answer will then
be nx to the n - 1.
02:02
Remember we've discussed this
before just by observation,looking at differentiation
from first principles.
02:08
Also we've done some
questions on this.
02:11
And we've also derived it
and proved to ourselves thatthis is true using differentiation
for first principles.
02:18
And as mathematicians, we like
proofs because that shows usthat what we're doing is the truth.

About the Lecture

The lecture Differentiation Basics by Batool Akmal is from the course Calculus Methods: Differentiation.

Included Quiz Questions

Differentiation of a function is used to find the gradient of the curve at/in ___________?

A point

An interval

Both in an interval and point

What is the derivative of a constant?

0

1

-1

x

1/x

Author of lecture Differentiation Basics

Batool Akmal

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